Complete elastic solution of pressurized thick cylindrical shells made of heterogeneous functionally graded materials

Assuming the Young's modulus vary nonlinearly in the radial direction, and the Poisson's ratio is constant, on the basis of plane elasticity theory (PET), the governing equations for axisymmetric thick cylindrical shells made of nonhomogeneous functionally graded materials (FGMs) subjected to internal and external pressure in general case are derived. The analytical solution of the Navier equations for real, double and complex roots and plane strain, plane stress and the cylinder with closed ends conditions are obtained. The radial stress, circumferential stress and radial displacement distributions depending on an inhomogeneity constant are compared with those of the homogeneous case, the solution using finite element method (FEM) and presented in the form of graphs.